Answer:
The Greek word kerygma means “proclamation.” In the New Testament, the term is often associated with preaching the Christian message, especially the fundamentals of the gospel. In the New Testament, John the Baptist was the one who prepared the way for Jesus the Messiah, “preaching in the wilderness of Judea” (Matthew 3:1).

When Jesus read from the scroll of Isaiah in the synagogue of Nazareth, He announced His mission to preach good news: “The Spirit of the Lord is upon me, because he has anointed me to proclaim good news to the poor. He has sent me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, to proclaim the year of the Lord’s favor” (Luke 4:18–19). Jesus had a kerygma to deliver on God’s behalf.

The apostle Paul used a form of the word kerygma when challenged his readers to preach the gospel: “How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them?” (Romans 10:14).

The word kerygma is also used by some theologians to refer to the entire teaching and ministry of Jesus. The use of this term was popularized by British scholar C. H. Dodd, who includes the following main aspects of the kerygma of Jesus:

1. The Age of Fulfillment has dawned, the “latter days” foretold by the prophets.

2. This has taken place through the birth, life, ministry, death and resurrection of Jesus Christ.

3. By virtue of the resurrection, Jesus has been exalted at the right hand of God as Messianic head of the new Israel.

4. The Holy Spirit in the church is the sign of Christ’s present power and glory.

5. The Messianic Age will reach its consummation in the return of Christ.

6. An appeal is made for repentance with the offer of forgiveness, the Holy Spirit, and salvation.
(source: http://www.afn.org/~afn52344/kerygma.html)

Second Corinthians 4:5 is a great summary of the preaching of the New Testament. Paul writes, “For what we preach is not ourselves, but Jesus Christ as Lord, and ourselves as your servants for Jesus’ sake.” This Christ-centered message may seem foolish to unbelievers, but Christ is the content of our kerygma: “We preach Christ crucified: a stumbling block to Jews and foolishness to Gentiles, but to those whom God has called, both Jews and Greeks, Christ the power of God and the wisdom of God” (1 Corinthians 1:23–24).